Simplify the following expression: $ x = \dfrac{a - 6}{-2} + \dfrac{9}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{a - 6}{-2} \times \dfrac{7}{7} = \dfrac{7a - 42}{-14} $ Multiply the second expression by $\dfrac{-2}{-2}$ $ \dfrac{9}{7} \times \dfrac{-2}{-2} = \dfrac{-18}{-14} $ Therefore $ x = \dfrac{7a - 42}{-14} + \dfrac{-18}{-14} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{7a - 42 - 18}{-14} $ $x = \dfrac{7a - 60}{-14}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{-7a + 60}{14}$